Finite Group Databasebeta

← C2×#19146039 #25969543

Subgroups — C2×#19146039 #25969543

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583507C211yesmaximal, characteristic, complemented
2C2×#14583503C211yesmaximal, characteristic
3#19146039C2116yesmaximal, direct product factor
4C2×#14583207C211yesmaximal, characteristic, complemented
5C2×#14583206C211yesmaximal, characteristic, complemented
6C2×#14583201C211yesmaximal, characteristic, complemented
7C2×#14583197C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583142C211yesmaximal, characteristic, complemented
10C2×#14583127C211yesmaximal, characteristic, complemented
11C2×#14583125C211yesmaximal, characteristic, complemented
12C2×#14583096C211yesmaximal, characteristic, complemented
13C2×#14583102C211yesmaximal, characteristic, complemented
14C2×#14583102C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#460C211yesmaximal, characteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583507—24no—
22#14583507C2218yescomplemented
23#14583503—24no—
24#14583503C2218yes—
25C2×#13063323C2211yescharacteristic
26C2×#13063320—21no—
27C2×#13063319—21no—
28C2×#13063317—21no—
29C2×#13063317C2211yescharacteristic
30C2×#13063316C2211yescharacteristic
31C2×#13063315—21no—
32C2×#13063306—21no—
33C2×#13063306—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063301C2211yescharacteristic
36C2×#13063297—21no—
37C2×#13063297—21no—
38C2×#13063296C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×C4×Dic86C2211yescharacteristic
41C2×D4×Dic43C2211yescharacteristic
42C2×D4×Dic43C2211yescharacteristic
43C2×#13063282C2211yescharacteristic
44#14583207C2218yescomplemented
45#14583206C2218yescomplemented
46#14583201C2218yescomplemented
47#14583197C2218yescomplemented
48#14583144C2218yescomplemented
49#14583142C2218yescomplemented
50#14583127C2218yescomplemented
51#14583125C2218yescomplemented
52#14583102C2218yescomplemented
53#14583102C2218yescomplemented
54#14583096C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×#13063249C2211yescharacteristic
67C2×#13063246C2211yescharacteristic
68C2×#13063246C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#127×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#460C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43—21no—
80C23×Dic43—21no—
81C23×Dic43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×#10621883—42no—
84C2×#10621883—42no—
85C2×#10621883C2314yes—
86C2×#10621883C2314yes—
87C2×#10621872—42no—
88C2×#10621872C2314yes—
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C2×C8×D43—42no—
92C2×C8×D43C2314yes—
93#13063323—22no—
94#13063323C2314yes—
95#13063320—28no—
96#13063319—28no—
97#13063317—22no—
98#13063317—28no—
99#13063317C2314yes—
100#13063316—22no—
101#13063316C2314yes—
102#13063315—28no—
103#13063306—28no—
104#13063306—28no—
105#13063305—22no—
106#13063305C2314yes—
107#13063301—22no—
108#13063301C2314yes—
109#13063297—28no—
110#13063297—28no—
111#13063296—22no—
112#13063296—22no—
113#13063296C2314yes—
114#13063296C2314yes—
115C4×Dic86—22no—
116C4×Dic86C2314yes—
117D4×Dic43—22no—
118D4×Dic43—22no—
119D4×Dic43C2314yes—
120D4×Dic43C2314yes—
121#13063282D414yes—
122#13063282C2314yes—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×Dic43⋊C4D411yescharacteristic
137C2×C22⋊Dic43—21no—
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4D411yescharacteristic
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063259C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063250C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×D4×C43—21no—
162C22×D4×C43—21no—
163C22×D4×C43C2311yescharacteristic
164C22×D4×C43C2311yescharacteristic
165C2×SD16×C43—42no—
166C2×SD16×C43—42no—
167C2×SD16×C43C2314yes—
168C2×SD16×C43C2314yes—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171#127×C43—22no—
172#127×C43C2314yes—
173C4×Q8×C43—22no—
174C4×Q8×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180#102×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C24×C43—21no—
184C23×D43C2×D411yescharacteristic
185C2×Q8×C43—21no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—21no—
191C2×D4×C43—24no—
192C2×D4×C43—24no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—82no—
198C2×D4×C43—82no—
199C2×D4×C43C2412yes—
200C2×D4×C43C2412yes—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—82no—
209C2×C22⋊D43—82no—
210C22×Dic43—24no—
211C22×Dic43—24no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—82no—
217C22×Dic43—82no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43C2×D412yes—
224C2×C4×D43C2412yes—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—21no—
228C2×Dic86C2412yes—
229SD16×C43—44no—
230SD16×C43—44no—
231C2×C8×C43—22no—
232C2×C8×C43—22no—
233C2×C8×C43C2412yes—
234C2×C8×C43C2412yes—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2412yes—
238C42×C43—24no—
239C42×C43C2×D412yes—
240C42×C43C2412yes—
241C22⋊Dic43—24no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244C22⋊Dic43—24no—
245#10621883—44no—
246#10621883—44no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4C2×D414yes—
250(C2×D43)⋊C4C2×D414yes—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—24no—
255C4⋊Dic43—24no—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258C4⋊Dic43C2412yes—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—24no—
266Dic43⋊C4C2×D414yes—
267Dic43⋊C4C2×D414yes—
268C4×Dic43—24no—
269C4×Dic43C2×D412yes—
270C4×Dic43C2412yes—
271C2×C43⋊C8—22no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8C2412yes—
274C2×C43⋊C8C2412yes—
275#10621872—44no—
276C8×D43—44no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43—42no—
283C23×C43—42no—
284C23×C43—42no—
285C23×C43C22×D411yescharacteristic
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43C22×D412yes—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—42no—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—84no—
300D4×C43—84no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43H(5,𝔽2)12yes—
311C2×C4×C432−1+412yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—84no—
314C22⋊D43—84no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328C2×Dic43C22×D412yes—
329C2×Dic43C22×D412yes—
330C2×Dic43C22×D412yes—
331C4×D43—24no—
332C4×D43—22no—
333C4×D43—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—42no—
337C8×C43—22no—
338C8×C43—22no—
339C43⋊C8—22no—
340C43⋊C8—22no—
341C2×#3260—431nomaximal, Sylow
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—84no—
349C22×C43—84no—
350C22×C43#53712yes—
351C22×C43#57712yes—
352C22×C43#57712yes—
353C22×C43C23×D411yescharacteristic
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—44no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43#53712yes—
363C4×C43C2×H(5,𝔽2)11yescharacteristic
364C4×C43C2×2−1+411yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—22no—
368Dic43—42no—
369Dic43—42no—
370Dic43—42no—
371Dic43—42no—
372C2×#541—431no—
373C2×#540—431no—
374#3260—4316no—
375C2×#479—431no—
376C2×#479—431no—
377C2×#478—431no—
378C2×#478—431no—
379C2×#468—431no—
380C2×#468—431no—
381C2×#465—431no—
382C2×#465—431no—
383C2×#460—431no—
384C2×#460D4311yescharacteristic, complemented
385C2×#461—431no—
386C2×#461—431no—
387C2×#424—431no—
388C2×C43—82no—
389C2×C43—82no—
390C2×C43#326014yescomplemented
391C2×C43C2×#53711yescharacteristic
392C2×C43C2×#57711yescharacteristic
393C2×C43C2×#57711yescharacteristic
394D43—42no—
395C22×SD16—431no—
396C22×SD16—431no—
397C22×SD16C2×D4311yescharacteristic
398C22×SD16C2×D4311yescharacteristic
399C22×M16—431no—
400C23×C8—431no—
401#541—438no—
402#541—864no—
403#540—438no—
404#540—864no—
405C2×C4⋊Q8—431no—
406C2×#127C2×D4311yescharacteristic
407C2×#126—861no—
408C2×#126—861no—
409C2×#125—431no—
410C2×#125—431no—
411C2×#125—861no—
412C2×#125—861no—
413C2×#123—861no—
414C2×#123—861no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×#121—431no—
418C2×#121—431no—
419C2×#121—861no—
420C2×#121—861no—
421C2×C4×Q8—431no—
422C2×C4×Q8C2×D4311yescharacteristic
423C2×C4×D4—431no—
424C2×C4×D4—431no—
425C2×#117—431no—
426#479—438no—
427#479—438no—
428#478—438no—
429#478—438no—
430#468—438no—
431#468—438no—
432#465—438no—
433#465—438no—
434#461—438no—
435#461—438no—
436#460—438no—
437#460C2×D4318yescomplemented
438C2×#107—431no—
439C2×#107—431no—
440C2×#106—431no—
441C2×#106—431no—
442#424—438no—
443C2×C4⋊C8—431no—
444C2×C4⋊C8—431no—
445C2×C4⋊C8—431no—
446C2×C4⋊C8C2×D4311yescharacteristic
447C2×#103—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102C2×D4311yescharacteristic
454C2×#102C2×D4311yescharacteristic
455C43C2×#326011yescharacteristic, complemented, Sylow
456C22×Q8—431no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—861no—
461C22×D4—861no—
462C22×D4C22×D4311yescharacteristic
463C22×D4C22×D4311yescharacteristic
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C2×SD16—42no—
468C2×SD16—42no—
469C2×SD16—434no—
470C2×SD16—434no—
471C2×SD16—1722no—
472C2×SD16—1722no—
473C2×SD16C22×D4314yes—
474C2×SD16C22×D4314yes—
475C2×M16—434no—
476C2×M16—1722no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—434no—
480C22×C8—1722no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C4⋊Q8—434no—
484C4⋊Q8—862no—
485#127—22no—
486#127C22×D4314yes—
487#126—868no—
488#126—868no—
489#125—434no—
490#125—434no—
491#125—868no—
492#125—862no—
493#125—868no—
494#125—862no—
495#123—868no—
496#123—868no—
497C22⋊Q8—434no—
498C22⋊Q8—434no—
499C22⋊Q8—862no—
500C22⋊Q8—862no—
501#121—434no—
502#121—434no—
503#121—868no—
504#121—868no—
505#121—862no—
506#121—862no—
507C4×Q8—22no—
508C4×Q8—434no—
509C4×Q8—862no—
510C4×Q8C22×D4314yes—
511C4×D4—434no—
512C4×D4—434no—
513C4×D4—862no—
514C4×D4—862no—
515#117—434no—
516#117—434no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—861no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—861no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4C22×D4311yescharacteristic
533C2×C22⋊C4—431no—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—21no—
542C2×C42—431no—
543C2×C42—861no—
544C2×C42C22×D4311yescharacteristic
545#107—434no—
546#107—434no—
547#106—434no—
548#106—434no—
549C4⋊C8—434no—
550C4⋊C8—434no—
551C4⋊C8—434no—
552C4⋊C8C22×D4314yes—
553#103—434no—
554#103—434no—
555#103—434no—
556#103—434no—
557#102—434no—
558#102—434no—
559#102C22×D4314yes—
560#102C22×D4314yes—
561C24—21no—
562C24—21no—
563C24—431no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—432no—
568C2×Q8—861no—
569C2×Q8—862no—
570C2×Q8—862no—
571C2×Q8C23×D4312yes—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—82no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—3442no—
585C2×D4—3442no—
586C2×D4C23×D4312yes—
587C2×D4C23×D4312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—864no—
596C22×C4—864no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—3442no—
604C22×C4—3442no—
605C22×C4D4×D4311yescharacteristic
606C22×C4D4×D4311yescharacteristic
607C22×C4C23×D4311yescharacteristic
608SD16—44no—
609SD16—44no—
610SD16—1724no—
611SD16—1724no—
612M16—1724no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—432no—
616C2×C8—432no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—1724no—
620C2×C8C23×D4312yes—
621C2×C8C23×D4312yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—434no—
625C4⋊C4—434no—
626C4⋊C4—432no—
627C4⋊C4—432no—
628C4⋊C4—432no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4—864no—
632C4⋊C4—864no—
633C4⋊C4—864no—
634C4⋊C4—864no—
635C4⋊C4—861no—
636C4⋊C4—861no—
637C4⋊C4—861no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4C23×D4312yes—
642C22⋊C4—434no—
643C22⋊C4—434no—
644C22⋊C4—864no—
645C22⋊C4—864no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C42—24no—
651C42—432no—
652C42—432no—
653C42—864no—
654C42D4×D4312yes—
655C42C23×D4312yes—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—432no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23C2×D4×D4311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—862no—
673Q8—862no—
674Q8—1722no—
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—42no—
681D4—84no—
682D4—84no—
683D4—3444no—
684D4—3444no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—864no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4C2×D4×D4312yes—
711C2×C4C2×D4×D4312yes—
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#1306337012yes—
714C2×C4#1306337212yes—
715C2×C4C24×D4311yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—862no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—84no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—1724no—
732C22#1458347812yes—
733C22#1458370512yes—
734C22#1458370912yes—
735C22C22×D4×D4311yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—862no—
741C4—862no—
742C4—862no—
743C4—1722no—
744C4—1722no—
745C4—1722no—
746C4—1722no—
747C4#1458347812yes—
748C4C2×#1306337011yescharacteristic
749C4C2×#1306337211yescharacteristic
750C2—82no—
751C2—82no—
752C2—1722no—
753C2#1914603914yesdirect product factor
754C2C2×#1458347811yescharacteristic
755C2C2×#1458370511yescharacteristic
756C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#460C2
socleC23×C43C22×D4
prime radicalC2×#14583503C2
hypercenterC2×#460D43
hypocenterC43C2×#3260
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583507C2semidirect
3. #19146039C2direct (N × H)
4. C2×#14583207C2semidirect
5. C2×#14583206C2semidirect
6. C2×#14583201C2semidirect
7. C2×#14583197C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583142C2semidirect
10. C2×#14583127C2semidirect
11. C2×#14583125C2semidirect
12. C2×#14583096C2semidirect
13. C2×#14583102C2semidirect
14. C2×#14583102C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#460C2semidirect
22. #14583507C22semidirect
44. #14583207C22semidirect
45. #14583206C22semidirect
46. #14583201C22semidirect
47. #14583197C22semidirect
48. #14583144C22semidirect
49. #14583142C22semidirect
50. #14583127C22semidirect
51. #14583125C22semidirect
52. #14583102C22semidirect
53. #14583102C22semidirect
54. #14583096C22semidirect
59. #14582924C22semidirect
73. C43×#460C22semidirect
384. C2×#460D43semidirect
390. C2×C43#3260semidirect
437. #460C2×D43semidirect
455. C43C2×#3260semidirect
753. C2#19146039direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145835072
C2×#145835032
#191460392
C2×#145832072
C2×#145832062
C2×#145832012
C2×#145831972
C2×#145831442
C2×#145831422
C2×#145831272
C2×#145831252
C2×#145830962
C2×#145831022
C2×#145829242
C2×C43×#4602
C2×#326043